Construction of a Pentagon on the cube Proof of Part I: Pentagon is Equilateral Proof of Part II: Pentagon is in One Plane Proof of Part III: Pentagon is Equiangular Proof of Part IV: Side of Dodec Form Apotome Construction of the Dodecahedron

Next, we use the Golden Ratio to divide 3 line segments, all of which starts from the midpoint of the square to a side of the square, with the greater segment closer to the midpoint. Lines that are divided this way are said to be divided in extreme and mean ratio. For convenience, we will refer to these points of division that utilizes the Golden Ratio as "Golden Ratio Division Points". We construct two Golden Ratio Division Points on one square, and one on the other. We arbitrarily choose to define two points on the left square, and define one on the right square. The reasons behind the procedures above will be explained in the subsequent proofs.

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